Question

Let Z be the set of integers. If $A=\{xϵZ:2^{(x+2)(x^2-5x+6)}\}=1$ and $B=\{xϵZ:-3<2x-1<9\}$, then the number of subsets of the set A $\times$ B, is :

• A. $2^{18}$
• B. $2^{10}$
• C. $2^{15}$
• D. $2^{12}$

Answer 1

The correct option is C $2^{15}$

$A=\{xϵz:2^{(x+2)(x^2-5x+6)}=1\}$

$2^{(x+2)(x^2-5x+6)}=2^0\Rightarrow x=-2,2,3$
$A=\{-2,2,3\}$

$B=\{xϵZ:-3<2x-1<9\}$

$B=\{0,1,2,3,4\}$

A $\times$ B has is 15 elements so number of subsets of A $\times$ B is $2^{15}$.